Theoretical Calculation and Simulation Analysis of Axial Static Stiffness of Double-Nut Ball Screw with Heavy Load and High Precision

Double-nut ball screws bear the action of bidirectional pretightening force, leading to the deformation of the contact area between the ball and the raceway. Under this condition, it is important to analyze and calculate the static stiffness of the ball screw. However, the conventional calculation method is inaccurate. Hence, a new method for the static stiffness analysis of a double-nut ball screw is proposed. Through the structural analysis of the ball screw and internal load distribution, a load deformation model was established based on the Hertzian contact theory. Through the load analysis of the ball screw, a static stiffness model of the ball screw was established and applied to a case study and a finite element simulation. The rigidity of THK double-nut ball screws used in the X-axis feed system of a high-stiffness heavy-duty friction stir welding robot (developed by the research group) was calculated. When the workload was lower than 1.1 × 10 4 N, the slope of the double-nut static stiffness curve increased significantly with the increase in the workload, and when the workload was greater than 1.1 × 10 4 N, its upward slope tended to stabilize. The simulated and experimental stiffness curves were in good agreement; when the external axial load was greater than 2.8 × 10 4 N, the stiffness value calculated using the finite element method gradually converged to the theoretical value; and when the axial load reached 3.0 × 10 4 N, the simulation and test curves matched well. The analysis method of the double-nut ball screw was found to be concise and accurate, and the stiffness curves calculated using the two methods were consistent. The simulation analysis of the static stiffness presented herein is expected to aid the design of double-nut ball screws of high-rigidity heavy-duty equipment.